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TEKNIK DIGITAL (A)TEKNIK DIGITAL (A)(TI 2104)(TI 2104)

Materi Kuliah ke-4

LOGIC GATE

OverviewOverview•• Binary logic and GatesBinary logic and Gates•• Boolean AlgebraBoolean Algebra

– Basic Properties– Algebraic Manipulation

•• Standard and Canonical FormsStandard and Canonical Forms– Minterms and Maxterms (Canonical forms)– SOP and POS (Standard forms)

•• KarnaughKarnaugh Maps (KMaps (K--Maps)Maps)– 2, 3, 4, and 5 variable maps– Simplification using K-Maps

•• KK--Map ManipulationMap Manipulation– Implicants: Prime, Essential– Don’t Cares

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Binary LogicBinary Logic

• Deals with binary variables that take 2 discrete values (0 and 1), and with logic operations

• Three basic logic operations: – AND, OR, NOT

• Binary/logic variables are typically represented as letters: A,B,C,…,X,Y,Z

Binary Logic FunctionBinary Logic Function

F(vars) = expression

Example: F(a,b) = a’•b + b ’G(x,y,z) = x•(y+z’)

set of binaryset of binaryvariablesvariables

nnOperators ( +, Operators ( +, ••, , ‘‘ ))nnVariablesVariablesnnConstants ( 0, 1 )Constants ( 0, 1 )nnGroupings (parenthesis)Groupings (parenthesis)

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Basic Logic OperatorsBasic Logic Operators

• 1-bit logic AND resembles binary multiplication:

0 • 0 = 0, 0 • 1 = 0,1 • 0 = 0, 1 • 1 = 1

• 1-bit logic OR resembles binary addition, except for one operation:

0 + 0 = 0, 0 + 1 = 1,1 + 0 = 1, 1 + 1 = 1 (? 102)

Truth Tables for logic operatorsTruth Tables for logic operatorsTruth table: tabular form that uniquely represents the relationship between the input variables of a function and its output

111001010000

F=A•BBA2-Input AND

111101110000

F=A+BBA2-Input OR

0110

F=A’ANOT

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Truth Tables (cont.)Truth Tables (cont.)

• Q: Let a function F() depend on nvariables. How many rows are there in the truth table of F() ?

A: 2n rows, since there are 2n possible binary patterns/combinations for the n variables

Logic GatesLogic Gates

• Logic gates are abstractions of electronic circuit components that operate on one or more input signals to produce an output signal.

2-Input AND 2-Input OR NOT (Inverter)

A A AB BF G H

F = AF = A••BB G = A+BG = A+B H = A’H = A’

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Timing DiagramTiming Diagram

A

B

F=A••B

G=A++B

H=A’

1

1

1

1

10

0

0

0

0

t0 t1 t2 t3 t4 t5 t6

Inputsignals

GateOutputSignals

Basic Assumption:Zero time forsignals topropagate Through gates

Transitions

Combinational Logic CircuitCombinational Logic Circuitfrom Logic Functionfrom Logic Function

• Consider function F = A’ + B•C’ + A’•B’• A combinational logic circuit can be constructed to implement F, by

appropriately connecting input signals and logic gates:– Circuit input signals à from function variables (A, B, C)– Circuit output signal à function output (F)– Logic gates à from logic operations

A

B

C

F

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Combinational Logic CircuitCombinational Logic Circuitfrom Logic Function (cont.)from Logic Function (cont.)

• In order to design a cost-effective and efficient circuit, we must minimize the circuit’s size (area) and propagation delay (time required for an input signal change to be observed at the output line)

• Observe the truth table of F=A’ + B•C’ + A’•B’ and G=A’ + B•C’

• Truth tables for F and G are identical à same function

• Use G to implement the logic circuit (less components)

1

0

1

0

1

0

1

0

C

0011

1111

0001

000 1

1110

1110

1100

1100

GFBA

Combinational Logic CircuitCombinational Logic Circuitfrom Logic Function (cont.)from Logic Function (cont.)

A

B

C

F

ABC

G

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TUGAS 3TUGAS 3

CARI DATA SHEET DARI IC CMOS & TTL SERIES DI INTERNET :

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74LS00, 74LS02, 74LS04, 74LS08, 74LS10, 74LS11, 74LS20, 74LS21, 74LS27, 74LS30, 74LS32, 74LS86